A general theoretical scheme for the evolution of a general discrete eigenvalue spectrum in a one-dimensional slab geometry neutron transport equation is described. To make a general procedure, we described the consistent scattering kernel. By using this scattering kernel, discrete eigenvalues are computed. Three methods are presented for the calculation of discrete eigenvalues, but the simplest one is chosen for the computation. Numerical results are presented in the tables. Results are discussed and compared with those already obtained using various methods available in the literature.